# Math Journal

Monday, 12/11/2023:

Refine some precalc notes.

Calc I new course info notes.

Notes in Precalc OneDrive notes to examples in Paul’s Math Notes on Unit Circle (Calc Trig Review)

Begin notes on double and half-angle formulas proofs.

Tuesday, 12/12/2023

Continue viewing/notes on double and half-angle formula proofs. In OneNote, with summary in LaTeX here, in Double and Half-Angle Formulas.

Wednesday, 12/13/2023

Work on How to Use the Double and Half Angle Formulas for Trigonometry (Precalculus - Trigonometry 28)

Try paper + FriXion instead of Rocketbook

Discover and work with SchoolYourself

Thursday, December 14, 2023

Continue double and half angles.

Weekend December 16-17, 2023

Began looking at Graph theory, in Introductory Discrete Mathematics (which is not the right tool for that or much of anything).

Found this Playlist for Graph Theory with Python, and began on first couple of videos.

Last item from searching for a review of Introduction to Graph Theory, which looks quite good.

Monday December 18, 2023

Scanned earlier notes on double and half angles

Finished viewing Solving the Königsberg Bridge Problem with Python

Read sample of Introduction to Graph Theory.

Tuesday, December 19, 2023

Preview some Python Graph Libraries

Continue working through Graph Theory with Python videos.

Hack around some in igraph (in source/CodeSolid/GraphWork)

Wednesday, December 20, 2023

Learn about magic X method – something I saw Professor Leonard do. Watched this: Factoring Quadratics…How?. Also Intro to Solving Quadratics (Leonard Precalc # 16)

In source/CodeSolid/sympy-tutorial, review some SymPy stuff, in branch calculus_testing, file Precalc_Demo.ipynb. Especially figure out how to change aspect ratio. :)

Thurs Dec 21, 2023

Spent some time memorizing half-angle and double angle formulas. Flash cards. Have them down pretty well, needs more attempts.

Some Desmos – trying to figure out triangle tool. Not good. Also tried Geogebra.

Friday Dec 22, 2023

Do Board problems from this video. And watch parts. Do first 3 probls today, leave some for later.

Saturday Dec 23, 2023

Review Half Angle / Double Angle Formulas

Sunday, Dec 24, 2023 NocheBuena

Looking for History of Math – popular math books

Read about the Quadrature of the Lune, mentioned in Journey Through Genius

Play with parametric equations and curves,here and here; and on desmos

Tuesday, December 26, 2023

Using the vertical line test, to test if an equation etc is a function. Watch Logarthims - How?. This is a prelude to this, which I should do next time… Solving logarithmic equations See notes here.

Next watched part of this, Euler’s constant and natural log, but a bit too fast.

Wednesday 27 Dec 2023

More Log review

Thursday 28 Dec 2023

Begin watching Propositional Logic. Pretty much like intro to logic, but with new symbols and with mathematical formulae for truth operators.

Friday 29 Dec 2023

Reading How to Ace Calculus

LogReview.ipynb, reworking markdown Log notes with some Python.

Did some quadratic equation problems.

Began reading The Transcendental Tangle, “that awful book”.

Saturday 30 Dec 2023

Work on exponential growth and decay functions from Transcendental Tangle.

A bit puzzling why we need \(e\) for this, so maybe follow up in future with Exponential Growth and Decay (prof Leonard)

Sympy already there in online python on CodeSolid.

Sunday 31 Dec 2023

Begin Intro Graph Theory.

One easy rate of decay problem Python.

Monday 1 Jan 2024

Finish Graphs chapter of Trudeau’s Introduction to Graph Theory (No exercises yet, except mentally on the first two.). A great read.

Tuesday 2 Jan 2024

Continue Trudeau, on to planar graphs.

More on exponentials and logarithms. Resources in notes. Begin with this Graphs of Exponential Functions (Prof Leonard)

limits.py function to create limits.

Wednesday 3 Jan 2024

Continue on Trudeau, finish planar graphs, on to Euler’s function.

Thurs 4 Jan 2024

Work a bit on Euler’s formula (Trudeau ~ pp 101-104), and on paper.

More quadratic work, solve 10 chat-gpt-generated factorable quadratics using “diamond method”.

Friday 5 Jan 2024

Reading Trudeau

Same 10 quadratic fns from Thursday, this time using quad. formula.

Sat 1/6/24

Reading Trudeau - coloring.

Some exponentials with common base. (From this video)

Sun 1/7

Reading Trudeau only.

Monday 1/8

Tomorrow’s the day!

“Finish up” rough reading (no exercises and portions of difficult passages skipped) of Trudeau.

Intro to Solving Logarithms and Exponentials with, as usual, problems worked by hand.

Take mandatory “sign off on policy” brightspace quiz.

Tuesday, 1/9

First day of Calculus class, Calc I, MAT 271 with Emma Scothorn. “Rain” day, met virtually.

Finished about 60% or so of the math homework for this week. So far so good. Online (Cengage + Webassign) tools are pretty good. “Master It” button is your friend.

Weds, 1/10/2014

Lot of time (about 5 hours) spent on homework 2.3. (Need to do more problems 9, 11, and 12 especially).

New calculator came in, learned how to plot and do some basic things.

Thursday 1/11

First day in person Calc I Mat 271. Units 2.2 and 2.3 on limits (review – I was ahead on homework this week). Calculator skills awful for a test, so…

When I got home figured out how to substitute values into an equation, to solve functions, where the cubed kerjigger is, how to not use minus when I mean negative since the device is dumb, and a few other things along the way. Need about an hour a day to get good at this.

Friday 1/12

A smackerel of How to Ace Calculus

Redo in class exercises from Thursday, and problematic homework from section 2.3. Nice!

Begin working on Homework and reading for section 2.4. Good progress.

Begin Reading Robert Stoll’s Set Theory and Logic (sample)

Saturday 1/13/2024

Continue on Stoll’s Set Theory

About 40 minutes or so on homework # 2.4, Continuity and One-Sided Limits. Made some progress.

Sunday 1/14

Continue homework # 2.4. Only one thorny problem left and one to redo.

Continue a bit of Stoll’s Set Theory.

Monday 1/15

Troubleshot nasty problem from yesterday – first answer was almost correct, but wrote “log” instead of “ln” in the answer box. :(

About halfway done with problem set 2.5 – so more than a week ahead. :)

Associated video on infinite limits, etc.

Tuesday 1/16/24

Holiday - no class.

Begin 3.1 work

Wednesday 1/17/24

Continue work on exercises 3.1

Continue reading Stoll

Thursday 1/18/24

Attend class

Meet with teacher re # 2.5 # 5

Finish 3.1 homework and attendance this week. :)

Friday 1/19/24

Reading up on Coq

Download signature assignment, having trouble with files

Finally able to begin work on this signature assignment and pretty much finish it. It’s in OneDrive and can be edited further on Microsoft 365.

Saturday 1/20/24

Reading Boyer on history of math.

Reading Russell Introduction to Mathematical Philosophy; first intro to Peano’s axioms.

Sunday 1/21/24

Continue reading Boyer, enjoyed especially ~ pp. 51-52 on Pythagoreans and Euclid’s cool method for doing a golden section of a line segment, which he called finding the extreme and mean segment. Began some reading and playing around with regular solids, found the formula for the interior angles of any regular polygon, given n = number of sides, interior angle formula is as below: $\( \frac{(n - 2) * 180}{n} \)$

E.g. for a triangle, \(\frac{(3 - 2) * 180}{3} = \frac{180}{3} =60^o\)

For a square, \(\frac{(4 - 2) * 180}{4} = \frac{360}{4} = 90^o\)

For a regular pentagon, \(\frac{(5 - 2) * 180}{5}= \frac{540}{5} = \frac{540}{5} = 108^o\)

Monday, January 22, 2024

Continue reading Boyer.

Tuesday, 1/23/24

Class Calc I

Review previous homework, 2.2 and most of 2.3. Retry problems and build list of problem areas.

Continue Boyer.

Wed, 1/24/24

Lots of homework, 2.3 and finish 2.4. Revisit some problem areas.

Some reading of Boyer.

Thursday 1/25/24

Class

Section 2.5 review

Reading Euclid’s Elements (Casey)

Friday 1/26/24

Reading Euclid’s Elements (Casey)

Section 3.1 review

Did study guide as a practice exam. Got 14 done, believed OK. So maybe a 93. Need to look at again.

Saturday 1/27/24

Reading Euclid and Boyer

Plan math BA see Google sheets

Sunday

Reading Euclid

An easy proof (my “first”) of “the bisectors of supplemental angles are 90 degrees apart.”

Monday

Go over results of Study guide “exam” on Friday. Send corrections to Emma Scothorn.

Learn how to work problems involving giving the equation of the line at a point, assuming you have a function and need to find the tangent line at some x value.